I guess for me, it were games that did something really new, mostly graphics-wise but also due to the immersion and pure fun they could provide;
The good..
Doom Wow what an improvement over Wolf3d, totally blew me away with what was possible, and lots of fun making my own levels, changing sound files, etc.
Half Life So different from previous FPS's, started more like an adventure really - and the physics of the engine were quite impressive.
Elite Ridiculously huge world to explore, lovely newtonian physics, sci-fi fan's wet dream
Syndicate Bold step to go for high-res with the limit to 16 colours, can you even fucking believe that they pulled that off ? Super fun game on top of that, cyber-noir future at it's best.
Another World What vectors, smooth, and nice gameplay too. Quite amazed.
Civilization (series) I guess the most amazing thing about this, is what a time-sink it is for me. Some things will always stand out, like China wanting to trade Rice for Plutonium.
Comanche The Voxel-based graphics were quite amazing, still are. Shame the technology took a second seat to polygon graphics.
A lot of C64 games really impressed me, but looking back it's hard to pick something that stands above the rest.
Honorary mentions:
RtcW MP Beta/Demo Played this one to death and beyond. Was playing it, and got news of the 2nd Gulf War starting through it's chat. Memorable moments. Kept playing way after the full game was released, with some other die-hard's.
Trade Wars (?) I'm not sure if this was the one, but a BBS doorgame, my first multi-player experience, where you could launch missiles against other players' worlds.
Horrible mentions, lest we never forget:
Oblivion Very hyped for this, but when I finally played it, it was more of a horse riding game, than anything else.
Fallout 3 Very hyped for this. But have you seen my father ? A middle-aged man ? Saddest thing is, playing this has made me hate the engine and interface so much, that I just cannot progress in FO:NV